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Subspace preserving completely positive maps

Johan Åberg
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Abstract

A class of quantum channels and completely positive maps (CPMs) are introduced and investigated. These, which we call subspace preserving (SP) CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve probability weights on a given orthogonal sum decomposition of the Hilbert space of a quantum system. Several equivalent characterizations of SP CPMs are proved and an explicit construction of all SP CPMs, is provided. For a subclass of the SP channels a construction in terms of joint unitary evolution with an ancilla system, is presented.

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Johan Åberg. 2003-12-16. Subspace preserving completely positive maps. https://doi.org/10.1016/j.aop.2004.04.013

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